Normally all web masters go for shared web hosting. In a shared hosting environment, the IP address of the server is shared among all the domains hosted on that server. If the server IP is penalized by a Search Engine on account of spamming or any other illegal activities, your website is also expected to be penalized.

Another situation where your website resides on a sever containing illegal adult contents, and that site is on the black list of Search Engines, your websites can also be banned. We would recommend to do a reverse lookup for the IP address and also check if the IP address is blocked by Spam cops.

Another situation, when your web host server is down and a Search Engine visits your website. It will not be able to crawl your website content and in-turn will report 404 error pages. This is not a good sign for SEO, as we never know when the Search Engines will re-visits your website and index your pages.

So its always safe to host your websites with a reputed hosting provider.
Qualities of good web hosting provider include 100% uptime ( Minimum 99% uptime ). We never know when a Search Engine visits your websites for crawling. Search Engines can visit your website at any time so it important to have your website up and running 24/7.

There is no clear way to identify a reputed web host, so its always recommended to google for some web host reviews and the proceed with sign up.

Conclusion

Host your websites with reputed web hosting providers and its also preferable to have an dedicated IP address.